Cloth | 2004 | ISBN: 0-691-12016-1
296 pp. | 6 x 9
This is the first comprehensive reference published on heat
equations associated with non self-adjoint uniformly elliptic
operators. The author provides introductory materials for those
unfamiliar with the underlying mathematics and background needed
to understand the properties of heat equations. He then treats Lp
properties of solutions to a wide class of heat equations that
have been developed over the last fifteen years. These primarily
concern the interplay of heat equations in functional analysis,
spectral theory and mathematical physics.
This book addresses new developments and applications of Gaussian
upper bounds to spectral theory. In particular, it shows how such
bounds can be used in order to prove Lp estimates for heat,
Schrodinger, and wave type equations. A significant part of the
results have been proved during the last decade.
The book will appeal to researchers in applied mathematics and
functional analysis, and to graduate students who require an
introductory text to sesquilinear form techniques, semigroups
generated by second order elliptic operators in divergence form,
heat kernel bounds, and their applications. It will also be of
value to mathematical physicists. The author supplies readers
with several references for the few standard results that are
stated without proofs.
El-Maati Ouhabaz is Professor of Analysis and Geometry at
Universite Bordeaux 1
Endorsements:
"This book is both an excellent introduction for those
learning about heat operators for the first time, and a reference
work for the mathematician searching for information. The author
has presented an especially lucid exposition of the subject."--Alan
McIntosh, Australian National University
"This book contains very interesting material, starting with
the basics and progressing to lively trends of current research."--Thierry
Coulhon, Cergy-Pontoise University
Series:London Mathematical Society Monographs, vol.30.
Series: Progress in Mathematics, Vol. 235
2005, VIII, 362 p. 6 illus., Hardcover
ISBN: 3-7643-4349-4
About this textbook
The transparency and power of geometric constructions has been a
source of inspiration to generations of mathematicians. The
beauty and persuasion of pictures, communicated in words or
drawings, continues to provide the intuition and arguments for
working with complicated concepts and structures of modern
mathematics. This volume contains a selection of articles
exploring geometric approaches to problems in algebra, algebraic
geometry and number theory.
Key topics include:
* Curves and their Jacobians
* Algebraic surfaces
* Moduli spaces, Shimura varieties
* Motives and motivic integration
* Number-theoretic applications, rational points
* Combinatorial aspects of algebraic geometry
* Quantum cohomology
* Arithmetic dynamical systems
The collection gives a representative sample of problems and most
recent results in algebraic and arithmetic geometry; the text can
serve as an intense introduction for graduate students and those
wishing to pursue research in these areas.
Contributors: I. Bauer, F. Bogomolov, N. Budur, F. Catanese, C.-L.
Chai, R. Cluckers, C. De Concini, J.S. Ellenberg, F. Grunewald, B.
Hassett, T. Hausel, F. Loeser, J. Pineiro, R. Pink, C. Procesi, M.
Spitzweck, P. Swinnerton-Dyer, L. Szpiro, H. Tamvakis, Y.
Tschinkel, T.J. Tucker, A. Venkatesh, and Y.G. Zarhin.
2005, XII, 168 p., Hardcover
ISBN: 0-387-22846-2
About this book
This monograph presents recent contributions to the topics of
almost periodicity and almost automorphy. Several new methods,
including the methods of invariant subspaces and uniform
spectrum, as well as various classical methods, such as fixed
point theorems, are used to obtain almost periodic and almost
automorphic solutions to some linear and non-linear evolution
equations and dynamical systems. Almost periodicity and almost
automorphy are also intensively developed on the more general
structures called fuzzy-number type spaces. They have further
potential applications to the study of differential equations,
which model the real-world problems governed by imprecision due
to uncertainty or vagueness, rather than randomness. In
conclusion, the author indicates several open problems and
directions for future research. This monograph is a great source
of information and inspiration for researchers and graduate
students from many mathematical fields.
Table of contents
Introduction and Preliminaries.- Almost Automorphic Vector-Valued
Functions.- Bibliographical Remarks and Open Problems.- Almost
Periodicity in Frechet Spaces.- Bibliographical Remarks and Open
Problems.- Differential Equations with Almost Automorphic
Solutions.- Bibliographical Remarks and Open Problems
Differential Equations with Almost Periodic Solutions.-
Bibliographical Remarks.- Almost Periodicity in Fuzzy Setting.-
Bibliographical Remarks. Almost Automorphy in Fuzzy Setting.-
Bibliographical Remarks.
Series: Lecture Notes in Physics, Vol. 662
2005, X, 297 p. Also available online., Hardcover
ISBN: 3-540-23900-6
About this book
This volume reflects the growing collaboration between
mathematicians and theoretical physicists to treat the
foundations of quantum field theory using the mathematical tools
of q-deformed algebras and noncommutative differential geometry.
A particular challenge is posed by gravity, which probably
necessitates extension of these methods to geometries with
minimum length and therefore quantization of space. This volume
builds on the lectures and talks that have been given at a recent
meeting on "Quantum Field Theory and Noncommutative Geometry."
A considerable effort has been invested in making the
contributions accessible to a wider community of readers - so
this volume will not only benefit researchers in the field but
also postgraduate students and scientists from related areas
wishing to become better acquainted with this field.
Table of contents
Noncommutative Geometry.- Poisson Geometry and Deformation
Quantization.- Applications in Physics.- Topological Quantum
Field Theory
Mathematics
Volume package: Computer Graphics & Geometric Modelling
2005, XIV, 959 p., Hardcover
ISBN: 1-85233-817-2
About this textbook
Possibly the most comprehensive overview of computer graphics as
seen in the context of geometric modelling, this two volume work
covers implementation and theory in a thorough and systematic
fashion. Computer Graphics and Geometric Modelling: Mathematics,
contains the mathematical background needed for the geometric
modeling topics in computer graphics covered in the first volume.
This volume begins with material from linear algebra and a
discussion of the transformations in affine & projective
geometry, followed by topics from advanced calculus &
chapters on general topology, combinatorial topology, algebraic
topology, differential topology, differential geometry, and
finally algebraic geometry. Two important goals throughout were
to explain the material thoroughly, and to make it self-contained.
This volume by itself would make a good mathematics reference
book, in particular for practitioners in the field of geometric
modelling. Due to its broad coverage and emphasis on explanation
it could be used as a text for introductory mathematics courses
on some of the covered topics, such as topology (general,
combinatorial, algebraic, and differential) and geometry (differential
& algebraic).
Table of contents
Linear Algebra Topics Affine Geometry Projective Geometry
Advanced Calculus Topics Point Set Topology Combinatorial
Topology Algebraic Topology Differential Topology Differential
Geometry Algebraic Geometry Appendices: Basic Algebra Basic
Linear Algebra Basic Calculus & Analysis Basic Complex
Analysis A Bit of Numerical Analysis
Series: Lecture Notes in Physics, Vol. 659
2005, XIV, 360 p. 34 illus. Also available online., Hardcover
ISBN: 3-540-23125-0
About this book
Application of the concepts and methods of topology and geometry have led to a deeper understanding of many crucial aspects in condensed matter physics, cosmology, gravity and particle physics. This book can be considered an advanced textbook on modern applications and recent developments in these fields of physical research. Written as a set of largely self-contained extensive lectures, the book gives an introduction to topological concepts in gauge theories, BRST quantization, chiral anomalies, sypersymmetric solitons and noncommutative geometry. It will be of benefit to postgraduate students, educating newcomers to the field and lecturers looking for advanced material.
Table of contents
Introduction and Overview (E. Bick, F.D. Steffen).- Topological Concepts in Gauge Theories (F. Lenz).- Aspects of BRST Quantization (J.W. van Holten).- Chiral Anomalies and Toplogy (J. Zinn-Justin).- Supersymmetric Solitons and Topology (M. Shifman).- Forces From Connes`Geometry (T. Schucker).
Series: Lecture Notes in Statistics, Vol. 179
2005, VI, 330 p., Softcover
ISBN: 0-387-20862-3
About this book
This volume contains a selection of papers presented at the Second Seattle Symposium in Biostatistics: Analysis of Correlated Data. The symposium was held in 2000 to celebrate the 30th anniversary of the University of Washington School of Public Health and Community Medicine. It featured keynote lectures by Norman Breslow, David Cox and Ross Prentice and 16 invited presentations by other prominent researchers. The papers contained in this volume encompass recent methodological advances in several important areas, such as longitudinal data, multivariate failure time data and genetic data, as well as innovative applications of the existing theory and methods. This volume is a valuable reference for researchers and practitioners in the field of correlated data analysis.
Table of contents
N. Breslow. Whither PQL?- O.B. Linton, E. Mammen, X. Lin and R.J. Carroll. Correlation and Marginal Longitudinal Kernel Nonparametric Regression.- G. Tang, R.J.A. Little and T.E. Raghunathan. Analysis of Multivariate Monotone Missing Data by a Pseudolikelihood Method.- L. Chen, L.J. Wei and M.I. Parzen. Quantile Regression for Correlated Observations.- Z. Feng, T. Braun and C. McCulloch. Small Sample Inference for Clustered Data.- W. Jiang and B.W. Turnbull. Some Applications of Indirect Inference to Longitudinal and Repeated Events Data.- D. Oakes. On Characterizing Joint Survivor Functions by Minima.- R.L. Prentice, Z. Moodie and J. Wu. Nonparametric Estimation of the Bivariate Survivor Function.- J.A. Wellner, Y. Zhang and H. Liu. A Semiparametric Regression Model for Panel Count Data: When do Pseudolikelihood Estimators Become Badly Inefficient?.- M. Gail and N. Chatterjee. Some Biases That May Affect Kin-Cohort Studies for Estimating the Risks from Identified Disease Genes.- J. Robins. Optimal Structural Nested Models for Optimal Sequential Decisions.